"The key used to encrypt and decrypt your vault data is encrypted with the Emergency Access contact’s public key, and can be decrypted only with their corresponding private key. When setting up Emergency Access, you are using the recipient’s public key, encrypting your vault key with that public key, and then LastPass stores that RSA-2048 encrypted data until it’s released after the waiting period you specify. Only the recipient can decrypt the data, so no one else can decrypt it without access to the private key of the recipient you’re sharing it with, which is encrypted with their master password key. This process is completely automated, with no action required by the end user, and ensures that the data is inaccessible by LastPass or outside parties."

What is a "key" for instance in this context. how can a key be both private and public? Who is "their" referring to in the first sentence - owner of vault or receiver of message?